What's the value of making the RL agent's output stochastic opposed to deterministic?
My understanding of your question is, you have 2 designs:


A deterministic policy that outputs 2 scalar for x and y respectively.
A value function that outputs the probability of each pixel in the 2D grid.


If you choose the max of softmax on (2.), you'll get the same deterministic policy as (1.), assuming there are some tie-breaking designs. So I don't think choosing the max of softmax is a great policy.

So, the question becomes "deterministic policy vs. value function". Since the value function have more information, we can have special designs on exploration.

In (1.), if you use $\epsilon$-greedy on the discrete output, It'll take a random move with $\epsilon$ probability. When exploring (instead of exploiting), all actions except the best action will have the same probability.

However, in (2.), the probability can act like a value function (the value of $Q(s, a) \forall a$ in a certain state $s$), and you can use something like upper confidence bound (UCB) instead of $\epsilon$-greedy. If you are using neural networks to output this probability distribution, you can add an entropy term in the loss function like in A3C to encourage exploration.